The invention relates to a method of resonance spectroscopy for the analysis of statistical properties of samples.
An example for a method for determining properties of an investigated mixture by resonance spectroscopy can be found in C. S. Johnson, “Diffusion ordered nuclear magnetic resonance spectroscopy: principles and applications”, in Progress in Nuclear Magnetic Resonance Spectroscopy 34 (1999), 203–256.
Resonance spectroscopy, in particular nuclear magnetic resonance spectroscopy, is a powerful tool for investigating samples (ref. /4/, /5/). E.g. the presence and the concentration of elements or compounds can be determined by means of resonance spectroscopy. In general, element or compound concentrations are determined by looking for characteristic resonance lines in the measured spectra and measuring the intensity of these lines.
In some applications, large amounts of samples need to be investigated in order to classify samples. For example, such a classification may be a separation of quality fractions of products in an industrial production process, or a healthy/non-healthy classification of blood samples in medicine. In these applications, statistical data analysis can be carried out, in particular pattern recognition (ref. /1/, /3/), in order to speed up the analysis.
According to the state of the art, the real part of each spectrum to be investigated is allocated to a point in an n-dimensional space (or point set), with n being a number of parameters extracted from each spectrum. These parameters may be, for example, intensity values at certain frequencies in the resonance spectra. All points are then displayed in the n-dimensional space. The points of spectra belonging to samples of the same classification can typically be found in a closed region of the n-dimensional space. Thus, by checking the position of a point in the n-dimensional space, the respective sample can—in principle—be classified.
However, typical spectra contain numerous spectral lines, and if the dimension n of the point set is too large; differences between the samples (resp. their spectra) are difficult to recognize. Fortunately, changes in different regions of the spectra are typically correlated. In this situation, principal component analysis can be performed in order to reduce the dimensionality of the relevant parameter space. Once relevant principal components (typically one, two or three) are known, the points representing the spectra may be transformed to a principal component basis, and classification of the samples is relatively easy then. A model for classification of samples using principal component analysis is disclosed in E. Holmes et al “Development of a model for classification of toxin-induced lesions using 1H NMR spectroscopy of urine combined with pattern recognition”.
In principle, all tools for an automated measurement of the spectra and the subsequent statistical analysis are available in the state of the art. Automated information acquisition would be very fast and inexpensive.
However, the reliability of such an automatic information acquisition in the state of the art is inadequate. The reason for this are random variances of measurement in the physical spectra recorded, in particular in the real parts of the spectra. Three of these variances are particularly important. First, there is an error due to imperfect base line correction. Second, the suppression of dominating but unwanted resonances of the samples (in particular solvent suppression in NMR) may be imperfect. And most important, there are phase errors in the recorded resonance spectra, deterring the spectra.
These three sources of unintended variances in the spectra superimpose the relevant variances in the spectra due to variances in the properties of the samples. Relevant variances can be mistaken for unintended statistical variances, or unintended statistical variances can be mistaken for an information containing variance. In effect, the relevant (i.e. information containing) variances are masked by the unintended variances to such a degree that an automatic analysis of the spectra becomes impossible. In the state of the art, there is no reliable tool for automatic correction or compensation of base line error, imperfect suppression of dominant but unwanted resonances and/or phase error. Corrections have to be performed manually. Automated analysis turns out to be insufficient. Even when manual corrections are carried out, different human operators still introduce deviations among the corrected spectra which are not caused by the physical properties of the respective samples. Known methods of phase corrections are published in references /6/–/9/.
It is the object of the invention to present a method of resonance spectroscopy which tolerates the above described unintended variances of measurement in the recorded resonance frequency spectra, in particular caused by phase errors, and allows reliable automated spectra analysis.